Photon-gluon colour orthogonality

In distinct-flavour quark annihilation, the one-photon exchange color charge tensor is ${\delta }_{ji}{\delta }_{kl}$, whereas the one-gluon tensor is ${\sum }_A{T}_{ji}^A{T}_{kl}^A$. Their inner product after the external color charge sum is ${\sum }_A\mathrm{tr}(T^A)\mathrm{tr}(T^A)=0$, since the fundamental gauge generators of $SU(3)$ are traceless. Thus the averaged squared scattering amplitude has no leading electromagnetic–strong interference term for this process. Fixed external color charge components, or processes with different exchange pairings, need not share this cancellation.